If you're a free-to-play or preferred status player, this does mean you're at some risk of losing your name. Characters below level 10 who haven't been played in 60 (free) or 90 (preferred) days will need to be renamed, as will characters below level 30 who haven't been played in 120 (free) or 180 (preferred) days. Characters 30 and above will be exempt across the board, as will all characters of subscribers. So you might be able to get your desired character name back! Or you'll find out that Xylophone is actually a level 31 Juggernaut, which is still kind of neat.
[Source: BioWare press release]